[R-sig-ME] Coefficients interpretation and plot

Wed Dec 29 23:14:52 CET 2010

Hi Luciano,

Quoting Luciano La Sala <lucianolasala at yahoo.com.ar>:

> Hi Jarrod,
>
> Thank you for the speedy reply. My issue seems to be the opposite: raw data
> indicates that A-eggs are a little smaller than B-eggs in 2006, while the
> GLMM (with Nest IDs as random intercepts) shows that A-eggs are a little
> larger than B-eggs.

I think this is what I meant too (if call the first to hatch as A-eggs).

I wonder if this difference comes from having included
> Nests as a random intercepts. Very far from being a statistician myself, the
> issue at hand baffles me.
>
> By the way, I only have three-egg clutches, and first, second, and third
> hatching chicks within each nest. Any ideas as to where this difference
> comes from?

In your output you have 130 observations from 55 nests: which is about  
2.46 eggs per nest rather than three. Is it possible there are NA's  
for some of the predictors?

Cheers,

Jarrod

>
> Best,
> Luciano
>
>
> ________________________________________
> De: Jarrod Hadfield [mailto:j.hadfield at ed.ac.uk]
> Enviado el: Wednesday, December 29, 2010 6:05 PM
> Para: Luciano La Sala
> CC: r-sig-mixed-models at r-project.org
> Asunto: Re: [R-sig-ME] Coefficients interpretation and plot
>
> Hi Luciano,
>
> If I understand you correctly, your issue is that the prediction for 
> the first egg in the year that is NOT (?) 2007 is greater than second 
> eggs in that year, yet the raw data indicate the opposite?
>
> I notice that you have less than 3 eggs for each nest. If there is a 
> (positive) relationship between clutch size and egg volume you could 
> get such a discrepancy. You could try putting clutch size in the 
> model. That being said, the offending coefficient is small with a 
> large p-value (0.35) so the discrepancy may not be that surprising.
>
> Also, I'm not sure what the state of play with pvals.func is. mcmcsamp 
> used to behave oddly, and from your output the fixed effects look OK, 
> but the 95% MCMC CI's for the variance components do not seem to 
> overlap the REML estimates. Its possible there on a different scale, 
> but I would check.
>
> Cheers,
>
> Jarrod
>
>
>
>
> Quoting Luciano La Sala <lucianolasala at yahoo.com.ar>:
>
>> Hello everyone,
>>
>> Since I'm not entirely sure this is THE list I should be referring too,
> feel
>> free to blow me off and refer me to another mailing list if necessary.
>> I am analyzing a small dataset using lmer from lme4 package. My model has
>> "egg volume" as dependent variable and "hatching order" and "year" as
>> dependent variables. The best fit model has these two variables plus their
>> interaction (hatching order*year). I included Nest_ID as random
> intercepts.
>> Output follows:
>>
>>> best <- lmer(EggVolume~HatchOrder+Year+HatchOrder*Year+(1|NestID), data =
>> Data)
>>> summary(best)
>>
>> Linear mixed model fit by REML
>>
>> Formula: EggVolume ~ HatchOrder + Year + HatchOrder * Year + (1 | NestID)
>>     Data: Data
>>     AIC BIC logLik deviance REMLdev
>>   736.1 759 -360.1    729.1   720.1
>>
>> Random effects:
>>   Groups   Name        Variance Std.Dev.
>>   NestID   (Intercept) 26.2931  5.1277
>>   Residual              6.2175  2.4935
>>
>> Number of obs: 130, groups: NestID, 55
>>
>> Fixed effects:
>>                        Estimate Std. Error t value
>> (Intercept)           79.7261     1.1350   70.24
>> HatchSecond           -0.7227     0.7758   -0.93
>> HatchThird            -4.8455     0.9112   -5.32
>> Year2007               3.5548     1.5750    2.26
>> HatchSecond:Year2007  -2.6914     1.0752   -2.50
>> HatchThird:Year2007   -2.7999     1.2294   -2.28
>>
>> Correlation of Fixed Effects:
>>              (Intr) HtchOS HtchOT Yr2007 HOS:Y2
>> HtchOrdrScn -0.277
>> HtchOrdrThr -0.229  0.388
>> Year2007    -0.721  0.199  0.165
>> HtcOS:Y2007  0.200 -0.722 -0.280 -0.299
>> HtcOT:Y2007  0.170 -0.287 -0.741 -0.301  0.415
>>
>> I used the "pvals.fnc" function in the "coda" package to estimate
> p-values.
>> Output follows:
>>
>>> pvals.fnc(best, nsim = 10000, ndigits = 4, withMCMC = FALSE,
>> addPlot=FALSE)
>>
>> $fixed
>>                    Estimate MCMCmean HPD95lower HPD95upper  pMCMC Pr(>|t|)
>> (Intercept)       79.7261  79.5990     77.687    81.5521 0.0001   0.0000
>> HatchSecond       -0.7227   0.1239     -2.630     2.8256 0.9468   0.3534
>> HatchThird        -4.8455  -4.3177     -7.391    -1.0711 0.0086   0.0000
>> Year2007           3.5548   3.9605      1.090     6.8664 0.0080   0.0258
>> HatchSecond:2007  -2.6914  -3.4393     -7.235     0.3782 0.0772   0.0136
>> HatchThird:2007   -2.7999  -3.6649     -7.768     0.5046 0.0830   0.0245
>>
>> $random
>>      Groups        Name Std.Dev. MCMCmedian MCMCmean HPD95lower HPD95upper
>> 1   NestID (Intercept)   5.1277     2.3265   2.3166     1.5388     3.1619
>> 2 Residual               2.4935     4.5507   4.5744     3.8179     5.4108
>>
>> I understand that, even in mixed models, one should not interpret main
>> effects' coefficients by themselves when a significant interaction is
>> present. Instead, coefficients of the main effect and the interaction term
>> should be added. In my example:
>>
>> # Coefficient for HatchSecond:Year2007: -0.7227 + (-2.6914) = -3.4141
>>
>> Then, in 2007 the volume of HatchSecond eggs was 3.41 units lower than
> that
>> of HathFirst eggs.
>>
>> # HatchThird:Year2007: -4.8455 + (-2.7999) = -7.6454
>>
>> Then, in 2007 the volumen of HatchThird eggs was 7.64 units lower than
> that
>> of HathFirst eggs.
>>
>> 1. Are these interpretations correct in the contest of mixed modeling?
>>
>> 2. When I plot my raw data (means of egg volume for each year and
> stratified
>> by hatching order), the plot looks good for 2007 (decreasing egg volumes
>> along the hatching sequence). However, HatchSecond eggs have a mean volume
>> slightly larger than that of HatchFirst eggs (80,02 vs. 79,47) which
> doesn't
>> reconcile with my GLMM: HatchSecond eggs from 2007 are 3.41 units lower
> than
>> that of HathFirst eggs.
>>
>> That said, I was wondering if this differences is due to the fact that the
>> GLMM includes a random effect (Nest) while plotting raw data ignores it.
>>
>> Thank you very much in advance!
>>
>> LFLS
>>
>> _______________________________________________
>> R-sig-mixed-models at r-project.org mailing list
>> https://stat.ethz.ch/mailman/listinfo/r-sig-mixed-models
>>
>>
>
>
>
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